Abstract: Based on the Lagrangian for the Gross –Pitaevskii
equation as derived by H. Sakaguchi and B.A Malomed [5] we have
derived a double well model for the nonlinear optical lattice. This
model explains the various features of nonlinear optical lattices.
Further, from this model we obtain and simulate the probability for
tunneling from one well to another which agrees with experimental
results [4].
Abstract: Recently T. C. Au-Yeung, C.Au, and P. C. W. Fung [2] have given the solution of the KdV equation [1] to the boundary condition , where b is a constant. We have further extended the method of [2] to find the solution of the KdV equation with asymptotic degeneracy. Via simulations we find both bright and dark Solitons (i.e. Solitons with opposite phases).